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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

Lower volume growth estimates for self-shrinkers of mean curvature flow


Authors: Haizhong Li and Yong Wei
Journal: Proc. Amer. Math. Soc. 142 (2014), 3237-3248
MSC (2010): Primary 53C44; Secondary 53C42
Published electronically: May 20, 2014
MathSciNet review: 3223379
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Abstract: We obtain a Calabi-Yau type volume growth estimate for complete noncompact self-shrinkers of the mean curvature flow. More precisely, every complete noncompact properly immersed self-shrinker has at least linear volume growth.


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Additional Information

Haizhong Li
Affiliation: Department of Mathematical Sciences, and Mathematical Sciences Center, Tsinghua University, 100084, Beijing, People’s Republic of China
Email: hli@math.tsinghua.edu.cn

Yong Wei
Affiliation: Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, People’s Republic of China
Email: wei-y09@mails.tsinghua.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-12037-5
Keywords: Self-shrinker, volume growth estimate, mean curvature flow
Received by editor(s): May 18, 2012
Received by editor(s) in revised form: September 18, 2012
Published electronically: May 20, 2014
Additional Notes: The authors were supported by NSFC No. 11271214 and Tsinghua University-K.U. Leuven Bilateral Scientific Cooperation Fund.
Communicated by: Lei Ni
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.